I think at Harvard it is possible, because they have a larger class size to fill.

But Yale and Stanford have much smaller classes. My GPA is 3.95 and my LSAT score is TBD. But if (God willing) I manage to get a good score, would I have any shot at getting in even though my list of extracurricular activities is shitty?

I would say that given a semi-strong PS and average LORs you have a very good chance at both Y and S if you score 175+ on the LSAT given your high GPA. Both are crapshoots a lot of the time, but it would surprise me if you got dinged at both with a really high LSAT and that GPA.